It is currently 23 Nov 2017, 05:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the sum of the digits of integer x, where x = 4^10* 5^13?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42326

Kudos [?]: 133105 [0], given: 12410

What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

### Show Tags

05 Nov 2017, 02:38
00:00

Difficulty:

55% (hard)

Question Stats:

72% (01:16) correct 28% (01:50) wrong based on 67 sessions

### HideShow timer Statistics

What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5
[Reveal] Spoiler: OA

_________________

Kudos [?]: 133105 [0], given: 12410

Manager
Joined: 18 May 2016
Posts: 151

Kudos [?]: 24 [1], given: 105

Location: India
GMAT 1: 710 Q48 V40
GPA: 4
WE: Marketing (Other)
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

### Show Tags

05 Nov 2017, 02:58
1
KUDOS
X= 2^20*5^13
= 10^13 *2^7
= 128*10^13

Sum of digits = 11
Option B

Sent from my A0001 using GMAT Club Forum mobile app

Kudos [?]: 24 [1], given: 105

Manager
Joined: 06 Aug 2017
Posts: 73

Kudos [?]: 13 [0], given: 27

GMAT 1: 610 Q48 V24
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

### Show Tags

05 Nov 2017, 12:15
1
This post was
BOOKMARKED
Bunuel wrote:
What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

$$x = 4^{10} * 5^{13} = 2^{20}*5^{13} = 10^{13}*2^7 = 10^{13}*128$$
Sum of the digits = 1+2+8 = 11

Hence B
_________________

-------------------------------------------------------------------------------
Kudos are the only way to tell whether my post is useful.

Kudos [?]: 13 [0], given: 27

Intern
Joined: 26 Jan 2017
Posts: 3

Kudos [?]: 0 [0], given: 5

Re: What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

### Show Tags

07 Nov 2017, 09:05
Since we are looking for the sum of the digits we can simplify this problem by removing the trailing zeros (zeros at the end of the number). Trailing zeros are added to a number when multiplied by 10.

Remember 10 = 2 * 5
Thus, in our problem 4^10*5^13 or:
2^20 * 5^13

As you can see we have the pair 2*5 thirteen times. We can remove 2^13 and 5^13 and work with the rest which is 2^7 = 128

1+2+8 = 11

Kudos [?]: 0 [0], given: 5

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1713

Kudos [?]: 914 [1], given: 5

Re: What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

### Show Tags

08 Nov 2017, 17:35
1
KUDOS
Expert's post
Bunuel wrote:
What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

We can simplify the given equation:

x = 4^10 x 5^13

x = 2^20 x 5^13

x = 2^7 x 2^13 x 5^13

x = 2^7 x 10^13

x = 128 x 10^13

We see that x is the number 128 followed by 13 zeros. Thus, the sum of the digits of x is 1 + 2 + 8 = 11.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 914 [1], given: 5

Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?   [#permalink] 08 Nov 2017, 17:35
Display posts from previous: Sort by